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Binomial

The binomial test is a non-parametric test for a difference in proportion between a sample and hypothesised proportion.

The requirements of the test are:

A dichotomous sample measured on a nominal or ordinal scale.

Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout. The dataset must contain a nominal or ordinal scale variable containing two groups.

When entering new data we recommend using New Dataset to create a new 1 variable (categorical) dataset ready for data entry.

Using the test

To start the test:

Excel 2007:Select any cell in the range containing the dataset to analyse, then click Distribution on the Analyse-it tab, then click Binomial.

Excel 97, 2000, 2002 & 2003:Select any cell in the range containing the dataset to analyse, then click Analyse on the Analyse-it toolbar, click Distribution then clickBinomial.

Click Variable then select the variable to compare.

Enter Hypothesised proportion as a value between 0 and 1.

Click Alternative hypothesis and select the alternative hypothesis to test:

X ≠ hypothesised proportion to test if the observed proportion of groups in X is not equal to the hypothesised proportion.

X > hypothesised proportion to test if the observed proportion of groups in X is greater than the hypothesised proportion.

X < hypothesised proportion to test if the observed proportion of groups in X is less than the hypothesised proportion.

Enter Confidence interval to calculate for the observed proportion. The level should be entered as a percentage between 50 and 100, without the % sign.

Click OK to run the test.

The report shows the number of observations analysed, number of missing values excluded, summary statistics for the sample, and the hypothesised proportion.

The observed proportion of the group in the sample and confidence interval are shown, with a hypothesis test. The p-value is the probability of rejecting the null hypothesis, that the proportion of the group in the sample is the same as the hypothesised proportion, when it is in fact true. A significant p-value implies the observed proportion in the sample differs from the hypothesised proportion.

METHOD An exact p-value and confidence interval are calculated (see [1] or [2]). The p-value and confidence interval both exploit the mathematical link between the Binomial and F distribution (Clopper-Pearson method) and so are able to provide exact p-values for small and large samples. The 2-tailed p-value is computed as 2 x 1-tailed p-value.